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Find the integral of the following equation: y = cos^2(x)

First convert y into a suitably form.cos(2x) = 1 - 2cos 2 (x)cos 2 x = (1-cos(2x))/2 integral of y = integral of (1-cos(2x))/2 = (1/2)*(x-(1/2)sin(2x)) + C = x/2 - sin(2x)/4 + C
MH
Answered by Marc H. • Maths tutor
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What is a geometric sequence?

A sequence is defined as a function with domain the set of the natural numbers, and codomain the set of the real numbers. A geometric sequence (a_n) is a sequence of the form: a_n = a_(n-1)*r, where r is a c...
GK
Answered by Georgios K. • Maths tutor
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The equation of a curve is xy^2= x^2 +1. Find dx/dy in terms of x and y, and hence find the coordinates of the stationary points on the curve.

dy/dx = (2x-y 2 )/(2xy)Stationary points: (1, root(2)) , (1, -root (2))
RS
Answered by Rishi S. • Maths tutor
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The function f has a local extreme at point (1,4). If f''(x)=3x^2+2x, then find f(0)?

A local extreme point would mean that f'(1)=0. Since integration is the inverse application of derivation, to obtain f'(x) function we integrate the f''(x) function. Bearing in mind the integration rule of i...
MT
Answered by Moris T. • Maths tutor
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Solve the simultaneous equation: 2x + y = 18, x - y = 6

First, we simply label the two equations as 'Equation 1' and 'Equation 2' respectively. So we have: Equation 1: 2x + y = 18and Equation 2: x - y = 6. In simultaneous equations, there are two variables: x and...
HM
Answered by Harry M. • Maths tutor
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